Sequence is the set of rules that guide the creation of a set. The rule of the sequence is to add 5, and the next three terms are 10, 15 and 20.
The first two terms of the sequence are given i.e.
[tex]T_1 =0[/tex] --- first term
[tex]T_2 = 5[/tex] --- second term
Because the first term is 0, then the sequence must be arithmetic.
Calculate the common difference using:
[tex]d = T_2 - T_1[/tex]
[tex]d = 5 - 0[/tex]
[tex]d = 5[/tex]
The nth term of an arithmetic sequence is calculated using:
[tex]T_n = T_1 +(n - 1)d[/tex]
So, we have:
[tex]T_n = 0 +(n - 1) \times 5[/tex]
[tex]T_n = 5(n - 1)[/tex]
So, the next three terms are:
[tex]T_3 = 5(3 - 1) =10[/tex]
[tex]T_4 = 5(4 - 1) =15[/tex]
[tex]T_5 = 5(5 - 1) =20[/tex]
Hence, the rule of the sequence is:
[tex]T_n = 5(n - 1)[/tex] or Add 5
The next three terms of the sequence are: 10, 15, 20
Read more about sequence at:
https://brainly.com/question/16977578
